When Brandon Meriweather first arrived at the University of Miami, he was known as “Little B” because he was a freshman with no status. By the time he established himself as an enforcer on the football field, his nickname had changed to “Killer B.”

“He literally would take people’s heads off,” said linebacker Jon Beason, who was a teammate of Meriweather’s at the U. “That’s the type of guy you want back there in the secondary.”

But it’s not necessarily the type of guy the NFL wants playing in its games these days. Meriweather, 31, was signed by the Giants on Sunday after injuries depleted the safety position. He arrives with the reputation of being one of the game’s most punishing hitters. He has been suspended twice by the league for illegal hits with his helmet and has violated the NFL’s rules against hitting defenseless opponents in the head six times.

Normally, the Giants might think twice about signing someone with that kind of baggage. But desperate times call for desperate measures. It’s no secret the Giants need help at safety, where injuries have sidelined most of those projected to man the positions left open by the departures of Antrel Rolle, Quintin Demps and Stevie Brown to free agency. Landon Collins, a rookie second-round pick, former cornerback Bennett Jackson, journeyman Jeromy Miles and backup Cooper Taylor all have been slowed by injuries. Mykkele Thompson, a rookie fifth-rounder, blew out his Achilles in Cincinnati.

Meriweather, a first-round pick of the Patriots in 2007, played 10 games with the Redskins last season before missing the rest of the year with a toe injury. He had yet to sign with another team, partly because of his injury and partly because of his reputation.

Coach Tom Coughlin acknowledged Meriweather, a two-time Pro Bowler, would bring “a degree of toughness to the secondary,” but wants it to be within the rules.

“The toughness part you want,” Coughlin said. “The penalties and the issues, you don’t want.”

That would be ideal, but it might be difficult to have one without the other when it comes to Meriweather, who has played a certain way for eight seasons and will be looking to make an instant impact with the Giants.

“I think every player you ever ask will say you play your game the way you play your game,” Meriweather said. “Do you play within the rules? Yes. When they make new rules, do you have to adjust a little bit? Yes. So, I’m going to play my game the way I play my game, but I’m also going to respect the rules.”

The Giants hope that doesn’t take away any of his physical presence because that’s what they need. The Bengals showed little respect for the Giants defense during Friday night’s preseason opener, fearing no repercussions for catching passes over the middle. Teams might think twice if Meriweather is back there.

“We were first-round picks because we were enforcers, because we did hit and because we were violent within the rules,” Beason said. “Having to make the transition from that is tough, especially at safety. But nine years in, he realizes the target area has changed.”

Jackson and Miles took most of the reps with the first team on Monday, but Meriweather also had his moments with the starters. He looked lost, which is natural for just his second practice.

Defensive coordinator Steve Spagnuolo knows little about Meriweather but suggested the player might temper his game after having waited nearly a month into training camp before signing with a team.

“It’s a very fine line for a coach, very fine line for a player in the league that we play in nowadays,” Spagnuolo said. “But it’s all about target, and it’s a low target area, a strike zone. We’re talking about from the chest down to the thigh. I think that a lot of aggressive players in this league have adjusted to that.”

Meriweather isn’t making any promises.

“I’m physical, and the great defenses of the Giants have always been physical,” he said. “So I’m thinking it will be a great fit.”